33. M&M’S An advertiser claims that the average percentage of brown M&M’S candies in a package of milk chocolate M&M’S is 13%. Suppose you randomly select a package of milk chocolate M&M’S that contains 55 candies and determine the proportion of brown candies in the package.

a. What is the approximate distribution of the sample proportion of brown candies in a package that contains 55 candies?

b. What is the probability that the sample percentage of brown candies is less than 20%?

c. What is the probability that the sample percentage exceeds 35%?

d. Within what range would you expect the sample proportion to lie about 95% of the time?